Average Error: 61.9 → 0
Time: 20.5s
Precision: 64
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]
↓
\[\Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-\left(2 + \frac{1}{2}\right)\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right))\]
\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))
↓
\Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-\left(2 + \frac{1}{2}\right)\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right))
double f() {
        double r2338629 = 1.0;
        double r2338630 = -r2338629;
        double r2338631 = 2.0;
        double r2338632 = r2338630 / r2338631;
        double r2338633 = 3.0;
        double r2338634 = sqrt(r2338633);
        double r2338635 = r2338634 / r2338631;
        double r2338636 = /* ERROR: no complex support in C */;
        double r2338637 = r2338636 * r2338636;
        double r2338638 = r2338637 * r2338636;
        double r2338639 = r2338638 * r2338636;
        double r2338640 = -r2338631;
        double r2338641 = 0.0;
        double r2338642 = /* ERROR: no complex support in C */;
        double r2338643 = r2338642 * r2338636;
        double r2338644 = r2338643 * r2338636;
        double r2338645 = r2338644 * r2338636;
        double r2338646 = r2338639 + r2338645;
        double r2338647 = 5.0;
        double r2338648 = /* ERROR: no complex support in C */;
        double r2338649 = r2338648 * r2338636;
        double r2338650 = r2338649 * r2338636;
        double r2338651 = r2338646 + r2338650;
        double r2338652 = 4.0;
        double r2338653 = /* ERROR: no complex support in C */;
        double r2338654 = r2338653 * r2338636;
        double r2338655 = r2338651 + r2338654;
        double r2338656 = 7.0;
        double r2338657 = /* ERROR: no complex support in C */;
        double r2338658 = r2338655 + r2338657;
        double r2338659 = /* ERROR: no complex support in C */;
        return r2338659;
}
↓
double f() {
        double r2338660 = 7.0;
        double r2338661 = 0.0;
        double r2338662 = /* ERROR: no complex support in C */;
        double r2338663 = 1.0;
        double r2338664 = -r2338663;
        double r2338665 = 2.0;
        double r2338666 = r2338664 / r2338665;
        double r2338667 = 3.0;
        double r2338668 = sqrt(r2338667);
        double r2338669 = r2338668 / r2338665;
        double r2338670 = /* ERROR: no complex support in C */;
        double r2338671 = 5.0;
        double r2338672 = /* ERROR: no complex support in C */;
        double r2338673 = r2338663 / r2338665;
        double r2338674 = r2338665 + r2338673;
        double r2338675 = -r2338674;
        double r2338676 = r2338669 + r2338661;
        double r2338677 = /* ERROR: no complex support in C */;
        double r2338678 = r2338670 * r2338677;
        double r2338679 = r2338672 + r2338678;
        double r2338680 = r2338670 * r2338679;
        double r2338681 = 4.0;
        double r2338682 = /* ERROR: no complex support in C */;
        double r2338683 = r2338680 + r2338682;
        double r2338684 = r2338683 * r2338670;
        double r2338685 = r2338662 + r2338684;
        double r2338686 = /* ERROR: no complex support in C */;
        return r2338686;
}

Error

Derivation

  1. Initial program 61.9

    \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0.0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0.0 i\right)\right))\]

  2. Simplified0

    \[\leadsto \color{blue}{\Re(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(\left(-2\right) + \frac{-1}{2}\right) + \left(0.0 + \frac{\sqrt{3}}{2}\right) i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right)\right) + \left(7 + 0.0 i\right)\right))}\]

  3. Final simplification0

    \[\leadsto \Re(\left(\left(7 + 0.0 i\right) + \left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(5 + 0.0 i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\left(-\left(2 + \frac{1}{2}\right)\right) + \left(\frac{\sqrt{3}}{2} + 0.0\right) i\right)\right)\right)\right) + \left(4 + 0.0 i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right))\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+ (+ (+ (+ (* (* (* (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (* (* (* (complex (- 2.0) 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (* (* (complex 5.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0))) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (* (complex 4.0 0.0) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))) (complex 7.0 0.0))))